BindsNET_Encoder_Demo.ipynb

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    "# BindsNet Encoders\n",
    "\n",
    "## 1. Table of Contents\n",
    "1. Table of Contents\n",
    "2. Overview\n",
    "2. Import Statements\n",
    "3. Encoders\n",
    "    1. Single Spike Encoders\n",
    "    2. Repeat Encoder\n",
    "    3. Poisson Encoders\n",
    "    4. Bernoulli Encoders\n",
    "    5. Rank Order Encoder\n",
    "\n",
    "## 2. Overview\n",
    "All of the encoders below transform an N dimensional input tensor into an N + 1 dimensional tensor, where the added dimension is time. The data fed into the encoders must all be floating point values. This is because some of the encoders perform divisions using the data that could approximate to fractional values."
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   "source": [
    "## 3. Import Statements"
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   "source": [
    "import os\n",
    "import torch\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from time import time as t\n",
    "\n",
    "from bindsnet.encoding import *"
   ]
  },
  {
   "source": [
    "## 3a. Single (Spike) Encoder\n",
    "### Summary\n",
    "The single (spike) encoder transforms the data into a tensor where the value at time 0 in the tensor for a given element in the input has a spike if the value is greater than the quantile cutoff. The closer to 1 the sparsity is, the more spikes will be permitted. A value of 0 means no spikes will be permitted.\n",
    "### Quantile Calculation\n",
    "For Numpy, the quantile is calculated as:\n",
    "```\n",
    "np.quantile(np.array([4, 3, 2, 1]),0) \n",
    "1\n",
    "np.quantile(np.array([4, 3, 2, 1]),0.25) \n",
    "1.75\n",
    "np.quantile(np.array([4, 3, 2, 1]),0.50) \n",
    "2.5\n",
    "np.quantile(np.array([4, 3, 2, 1]),0.75) \n",
    "3.25\n",
    "np.quantile(np.array([4, 3, 2, 1]),1) \n",
    "4\n",
    "```"
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     "metadata": {}
    },
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Input Datum:\n[[80. 70. 60.]\n [50. 40. 30.]\n [20. 10.  0.]]\n\nEncoded Datum w/ Sparsity of 0.25:\n[[[1 1 0]\n  [0 0 0]\n  [0 0 0]]]\n\nEncoded Datum w/ Sparsity of 0.5:\n[[[1 1 1]\n  [1 0 0]\n  [0 0 0]]]\n\nEncoded Datum w/ Sparsity of 0.75:\n[[[1 1 1]\n  [1 1 1]\n  [0 0 0]]]\n\nEncoded Datum w/ Sparsity of 1:\n[[[1 1 1]\n  [1 1 1]\n  [1 1 0]]]\n\n"
     ]
    }
   ],
   "source": [
    "# time is the total sample duration in ms\n",
    "# set to 1 for this example because steps after the first will not generate spikes\n",
    "time = 1\n",
    "\n",
    "# dt is the step size within the sample duration in ms\n",
    "dt = 1.0\n",
    "\n",
    "# num_steps is how many steps are generated based on the time and dt values\n",
    "num_steps = int(time/dt)\n",
    "\n",
    "# input data\n",
    "train_image = torch.FloatTensor([[80,70,60],[50,40,30],[20,10,0]])\n",
    "\n",
    "# show input image\n",
    "plt.matshow(train_image, cmap='binary')\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Y')\n",
    "plt.title('Input Image')\n",
    "plt.show()\n",
    "\n",
    "# print train data\n",
    "print(\"Input Datum:\")\n",
    "print(train_image.numpy())\n",
    "print()\n",
    "\n",
    "# sparsity of spikes (1 for all spikes, 0 for no spikes)\n",
    "\n",
    "# spikes over the 0.75 quantile will be permitted\n",
    "sparsity = 0.25\n",
    "encoder = SingleEncoder(time=time, dt=dt,sparsity=sparsity)\n",
    "encoded_image = encoder(train_image)\n",
    "print(\"Encoded Datum w/ Sparsity of 0.25:\")\n",
    "print(encoded_image.numpy())\n",
    "print()\n",
    "\n",
    "# spikes over the 0.5 quantile will be permitted\n",
    "sparsity = 0.5\n",
    "encoder = SingleEncoder(time=time, dt=dt,sparsity=sparsity)\n",
    "encoded_image = encoder(train_image)\n",
    "print(\"Encoded Datum w/ Sparsity of 0.5:\")\n",
    "print(encoded_image.numpy())\n",
    "print()\n",
    "\n",
    "# spikes over the 0.25 quantile will be permitted\n",
    "sparsity = 0.75\n",
    "encoder = SingleEncoder(time=time, dt=dt,sparsity=sparsity)\n",
    "encoded_image = encoder(train_image)\n",
    "print(\"Encoded Datum w/ Sparsity of 0.75:\")\n",
    "print(encoded_image.numpy())\n",
    "print()\n",
    "\n",
    "# all spikes will be permitted\n",
    "sparsity = 1\n",
    "encoder = SingleEncoder(time=time, dt=dt,sparsity=sparsity)\n",
    "encoded_image = encoder(train_image)\n",
    "print(\"Encoded Datum w/ Sparsity of 1:\")\n",
    "print(encoded_image.numpy())\n",
    "print()"
   ]
  },
  {
   "source": [
    "## 3b. Repeat Encoder\n",
    "### Summary\n",
    "Repeats the same datum vector for `time/dt` timesteps\n"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "# time is the total sample duration in ms\n",
    "time = 3\n",
    "\n",
    "# dt is the step size within the sample duration in ms\n",
    "dt = 1.0\n",
    "\n",
    "# num_steps is how many steps are generated based on the time and dt values\n",
    "num_steps = int(time/dt)\n",
    "\n",
    "# input data\n",
    "train_image = torch.FloatTensor([[80,70,60],[50,40,30],[20,10,0]])\n",
    "\n",
    "# show input image\n",
    "plt.matshow(train_image, cmap='binary')\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Y')\n",
    "plt.title('Input Image')\n",
    "plt.show()\n",
    "\n",
    "# print train data\n",
    "print(\"Input Datum:\")\n",
    "print(\"======================\")\n",
    "print(train_image)\n",
    "print()\n",
    "\n",
    "# create encoder and encode input\n",
    "encoder = RepeatEncoder(time=time, dt=dt)\n",
    "train_image = torch.FloatTensor([[80,70,60],[50,40,30],[20,10,0]])\n",
    "encoded_image = encoder(train_image)\n",
    "print(\"Encoded Datum:\")\n",
    "print(\"======================\")\n",
    "print(encoded_image.numpy())\n",
    "print()\n",
    "\n",
    "# Look at input spiking activity.\n",
    "encoded_image = np.reshape(encoded_image,(num_steps,train_image.nelement())).T\n",
    "plt.matshow(encoded_image, cmap='binary')\n",
    "plt.xlabel('Time')\n",
    "plt.ylabel('Neuron index')\n",
    "plt.title('Encoded Image Spiking Activity')\n",
    "plt.yticks(np.arange(train_image.nelement()))\n",
    "plt.xticks(np.arange(num_steps))\n",
    "plt.show()"
   ]
  },
  {
   "source": [
    "## 3c. Poisson Encoder\n",
    "\n",
    "### Summary\n",
    "Generates Poisson-distributed spike trains based on input intensity. Inputs must be non-negative, and give the firing rate in Hz. Inter-spike intervals (ISIs) for non-negative data incremented by one to avoid zero intervals while maintaining ISI distributions.\n",
    "\n",
    "### Limitations\n",
    "* Inputs must be non-negative\n",
    "* Inputs must be floating point numbers (otherwise the rate will zero out)\n",
    "\n",
    "### Rate Calculation\n",
    "\n",
    "1. Compute firing rates in seconds as a function of data intensity\n",
    "    * rate = (1 / input_intensity) * (1000 / dt)\n",
    "    * higher intensity -> lower inter-spike interaval\n",
    "    * dt = simulation time step\n",
    "2. Create Poisson distribution and sample inter-spike intervals\n",
    "    * `torch.distributions.Poisson()` used to generate samples\n",
    "    * `time/dt` samples are taken for each input element based on the probability density function (pdf) of a Poisson distribution\n",
    "        * Vales near the rate (lambda) more likely to occur\n",
    "        * The higher the rate, the more varied the data will be\n",
    "    * if any samples produced 0, set them to 1\n",
    "3. Incrementally add all of the samples generated for each input element\n",
    "    * this produces indexes of where to set the spike outputs for each element in the spikes array\n",
    "    * if any samples are greater than `time/dt`, set them to 0 because they are outside of the sample duration\n",
    "4. Create tensor of spikes\n",
    "    * for each of the indexes produced, set the corresponding indexes in the spike tensor to 1\n",
    "    * given an input tensor with dimsnions X x Y, the output tensor has dimensions (time/dt + 1) x X x Y\n",
    "    * remove the first row of spikes because they are all set to 1\n",
    "5. Summary\n",
    "    * samples = time/dt\n",
    "    * rate = (1/intensity)*(1000/dt)\n",
    "    * intervals = torch.distributions.Poisson(rate=rate).sample(sample_shape=samples)\n",
    "    * times = torch.cumsum(intervals,dim=0).long()\n",
    "    * spikes\\[times] = 1\n",
    "\n",
    "### Poisson Distribution\n",
    "\n",
    "![Poisson Probability Function](https://wikimedia.org/api/rest_v1/media/math/render/svg/c22cb4461e100a6db5f815de1f44b1747f160048)\n",
    "\n",
    "![Poisson Probability Graph Function](https://upload.wikimedia.org/wikipedia/commons/thumb/1/16/Poisson_pmf.svg/325px-Poisson_pmf.svg.png)\n",
    "\n",
    "where\n",
    "* k is the number of occurrences\n",
    "* λ is the rate (mean number of occurrences in the interval)\n",
    "\n",
    "(Source [wikipedia.org](https://en.wikipedia.org/wiki/Poisson_distribution))"
   ],
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      "Input Datum:\n======================\n[[100.   75.   50. ]\n [ 25.   15.   10. ]\n [  5.    2.5   0. ]]\n\nRates for Each Element:\n======================\nRate for 100.0: 10 Hz (Approx. 1 spike per 1.0 time steps.)\nRate for 75.0: 7 Hz (Approx. 1 spike per 1.33 time steps.)\nRate for 50.0: 5 Hz (Approx. 1 spike per 2.0 time steps.)\nRate for 25.0: 2 Hz (Approx. 1 spike per 4.0 time steps.)\nRate for 15.0: 2 Hz (Approx. 1 spike per 6.67 time steps.)\nRate for 10.0: 1 Hz (Approx. 1 spike per 10.0 time steps.)\nRate for 5.0: 0 Hz (Approx. 1 spike per 20.0 time steps.)\nRate for 2.5: 0 Hz (Approx. 1 spike per 40.0 time steps.)\nRate for 0.0: 0 Hz (Approx. 1 spike per 0 time steps.)\n\nEncoded Datum:\n======================\n"
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xlink:href=\"#mb27cafc35e\" y=\"38.99625\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_16\">\r\n      <!-- 15 -->\r\n      <g transform=\"translate(304.646125 29.916562)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-49\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-53\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_17\">\r\n     <g id=\"line2d_33\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"328.864625\" xlink:href=\"#m1789224ae0\" y=\"199.70025\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"line2d_34\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"328.864625\" xlink:href=\"#mb27cafc35e\" y=\"38.99625\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_17\">\r\n      <!-- 16 -->\r\n      <g transform=\"translate(322.502125 29.916562)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-49\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-54\"/>\r\n      </g>\r\n   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style=\"stroke:#000000;stroke-width:0.8;\" x=\"364.576625\" xlink:href=\"#mb27cafc35e\" y=\"38.99625\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_19\">\r\n      <!-- 18 -->\r\n      <g transform=\"translate(358.214125 29.916562)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-49\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-56\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_20\">\r\n     <g id=\"line2d_39\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"382.432625\" xlink:href=\"#m1789224ae0\" y=\"199.70025\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"line2d_40\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"382.432625\" xlink:href=\"#mb27cafc35e\" y=\"38.99625\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_20\">\r\n      <!-- 19 -->\r\n      <g transform=\"translate(376.070125 29.916562)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-49\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-57\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_21\">\r\n     <g id=\"line2d_41\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"400.288625\" xlink:href=\"#m1789224ae0\" y=\"199.70025\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"line2d_42\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"400.288625\" xlink:href=\"#mb27cafc35e\" y=\"38.99625\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_21\">\r\n      <!-- 20 -->\r\n      <g transform=\"translate(393.926125 29.916562)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-50\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_22\">\r\n     <g id=\"line2d_43\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"418.144625\" xlink:href=\"#m1789224ae0\" y=\"199.70025\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"line2d_44\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"418.144625\" xlink:href=\"#mb27cafc35e\" y=\"38.99625\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_22\">\r\n      <!-- 21 -->\r\n      <g transform=\"translate(411.782125 29.916562)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-50\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-49\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_23\">\r\n     <g id=\"line2d_45\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"436.000625\" xlink:href=\"#m1789224ae0\" y=\"199.70025\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"line2d_46\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"436.000625\" xlink:href=\"#mb27cafc35e\" y=\"38.99625\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_23\">\r\n      <!-- 22 -->\r\n      <g transform=\"translate(429.638125 29.916562)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-50\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-50\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_24\">\r\n     <g id=\"line2d_47\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"453.856625\" xlink:href=\"#m1789224ae0\" y=\"199.70025\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"line2d_48\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"453.856625\" xlink:href=\"#mb27cafc35e\" y=\"38.99625\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_24\">\r\n      <!-- 23 -->\r\n      <g transform=\"translate(447.494125 29.916562)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-50\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-51\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_25\">\r\n     <g id=\"line2d_49\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"471.712625\" xlink:href=\"#m1789224ae0\" y=\"199.70025\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"line2d_50\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"471.712625\" xlink:href=\"#mb27cafc35e\" y=\"38.99625\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_25\">\r\n      <!-- 24 -->\r\n      <g transform=\"translate(465.350125 29.916562)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-50\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-52\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_26\">\r\n     <g id=\"line2d_51\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"489.568625\" xlink:href=\"#m1789224ae0\" y=\"199.70025\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"line2d_52\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"489.568625\" xlink:href=\"#mb27cafc35e\" y=\"38.99625\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_26\">\r\n      <!-- 25 -->\r\n      <g transform=\"translate(483.206125 29.916562)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-50\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-53\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_27\">\r\n     <g id=\"line2d_53\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"507.424625\" xlink:href=\"#m1789224ae0\" y=\"199.70025\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"line2d_54\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"507.424625\" xlink:href=\"#mb27cafc35e\" y=\"38.99625\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_27\">\r\n      <!-- 26 -->\r\n      <g transform=\"translate(501.062125 29.916562)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-50\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-54\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_28\">\r\n     <g id=\"line2d_55\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"525.280625\" xlink:href=\"#m1789224ae0\" y=\"199.70025\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"line2d_56\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"525.280625\" xlink:href=\"#mb27cafc35e\" y=\"38.99625\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_28\">\r\n      <!-- 27 -->\r\n      <g transform=\"translate(518.918125 29.916562)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-50\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-55\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_29\">\r\n     <g id=\"line2d_57\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"543.136625\" xlink:href=\"#m1789224ae0\" y=\"199.70025\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"line2d_58\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"543.136625\" xlink:href=\"#mb27cafc35e\" y=\"38.99625\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_29\">\r\n      <!-- 28 -->\r\n      <g transform=\"translate(536.774125 29.916562)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-50\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-56\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_30\">\r\n     <g id=\"line2d_59\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"560.992625\" xlink:href=\"#m1789224ae0\" y=\"199.70025\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"line2d_60\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"560.992625\" xlink:href=\"#mb27cafc35e\" y=\"38.99625\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_30\">\r\n      <!-- 29 -->\r\n      <g transform=\"translate(554.630125 29.916562)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-50\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-57\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_31\">\r\n     <g id=\"line2d_61\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"578.848625\" xlink:href=\"#m1789224ae0\" y=\"199.70025\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"line2d_62\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"578.848625\" xlink:href=\"#mb27cafc35e\" y=\"38.99625\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_31\">\r\n      <!-- 30 -->\r\n      <g transform=\"translate(572.486125 29.916562)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-51\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_32\">\r\n     <g id=\"line2d_63\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"596.704625\" xlink:href=\"#m1789224ae0\" y=\"199.70025\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"line2d_64\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"596.704625\" xlink:href=\"#mb27cafc35e\" y=\"38.99625\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_32\">\r\n      <!-- 31 -->\r\n      <g transform=\"translate(590.342125 29.916562)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-51\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-49\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_33\">\r\n     <g id=\"line2d_65\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"614.560625\" xlink:href=\"#m1789224ae0\" y=\"199.70025\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"line2d_66\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"614.560625\" xlink:href=\"#mb27cafc35e\" y=\"38.99625\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_33\">\r\n      <!-- 32 -->\r\n      <g transform=\"translate(608.198125 29.916562)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-51\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-50\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_34\">\r\n     <g id=\"line2d_67\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"632.416625\" xlink:href=\"#m1789224ae0\" y=\"199.70025\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"line2d_68\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"632.416625\" xlink:href=\"#mb27cafc35e\" y=\"38.99625\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_34\">\r\n      <!-- 33 -->\r\n      <g transform=\"translate(626.054125 29.916562)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-51\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-51\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_35\">\r\n     <g id=\"line2d_69\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"650.272625\" xlink:href=\"#m1789224ae0\" y=\"199.70025\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"line2d_70\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" 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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "# time is the total sample duration in ms\n",
    "time = 500\n",
    "\n",
    "# dt is the step size within the sample duration in ms\n",
    "dt = 10\n",
    "\n",
    "# num_steps is how many steps are generated based on the time and dt values\n",
    "num_steps = int(time/dt)\n",
    "\n",
    "# input data\n",
    "train_image = torch.FloatTensor([[100,75,50],[25,15,10],[5,2.5,0]])\n",
    "\n",
    "# show input image\n",
    "plt.matshow(train_image, cmap='binary')\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Y')\n",
    "plt.title('Input Image')\n",
    "plt.show()\n",
    "\n",
    "# print train data\n",
    "print(\"Input Datum:\")\n",
    "print(\"======================\")\n",
    "print(train_image.numpy())\n",
    "print()\n",
    "\n",
    "# rates\n",
    "print(\"Rates for Each Element:\")\n",
    "print(\"======================\")\n",
    "for element in train_image.flatten():\n",
    "    period = ((1/element.item())*(1000/dt)) if (element.item() != 0) else 0\n",
    "    rate = 1 / period if period != 0 else 0\n",
    "    \n",
    "    print(\"Rate for \"+str(element.item())+\":\",round(rate*dt),\"Hz\",\"(Approx. 1 spike per\",round(period,2),\"time steps.)\")\n",
    "print()\n",
    "\n",
    "# create encoder and encode input\n",
    "encoder = PoissonEncoder(time=time, dt=dt)\n",
    "encoded_image = encoder(train_image)\n",
    "print(\"Encoded Datum:\")\n",
    "print(\"======================\")\n",
    "\n",
    "# Look at input spiking activity.\n",
    "encoded_image = np.reshape(encoded_image,(num_steps,train_image.nelement())).T\n",
    "plt.matshow(encoded_image, cmap='binary')\n",
    "plt.xlabel('Time')\n",
    "plt.ylabel('Neuron index')\n",
    "plt.title('Encoded Image Spiking Activity')\n",
    "plt.yticks(np.arange(train_image.nelement()))\n",
    "plt.xticks(np.arange(num_steps))\n",
    "plt.show()"
   ]
  },
  {
   "source": [
    "## 3d. Bernoulli Encoder\n",
    "### Summary\n",
    "Generates Bernoulli-distributed spike trains based on input intensity. Inputs must be non-negative. Spikes correspond to successful Bernoulli trials, with success probability equal to (normalized in \\[0, 1]) input value. A maximum probability can be set using the `max_prob` argument\n",
    "\n",
    "### Limitations\n",
    "* Inputs must be non-negative\n",
    "* Inputs must be floating point numbers (otherwise the rate will zero out)\n",
    "\n",
    "### Bernoulli Trial Calculation\n",
    "1. Inputs are normalized based on the max intensity\n",
    "    * The highest intensity will have a probability of 1 and always spike\n",
    "    * An intensity of 0 will have a probability of 0 and never spike\n",
    "2. The spike tensor is generated using `torch.bernoulli()` to generate the random samples\n",
    "    * Highest intensity will always produce 1, lower intensities will generate 1's based on their scale against the highest intensity"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 288x288 with 1 Axes>",
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      "Input Datum:\n======================\ntensor([[80., 70., 60.],\n        [50., 40., 30.],\n        [20., 10.,  0.]])\n\nProbabilities of Spiking for Each Element per time step:\n======================\nProbability for 80.0 to spike per time step: 100%\nProbability for 70.0 to spike per time step: 88%\nProbability for 60.0 to spike per time step: 75%\nProbability for 50.0 to spike per time step: 62%\nProbability for 40.0 to spike per time step: 50%\nProbability for 30.0 to spike per time step: 38%\nProbability for 20.0 to spike per time step: 25%\nProbability for 10.0 to spike per time step: 12%\nProbability for 0.0 to spike per time step: 0%\n\nEncoded Datum:\n======================\n\n"
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xlink:href=\"#m34329f3dd6\" y=\"38.99625\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_16\">\r\n      <!-- 15 -->\r\n      <g transform=\"translate(304.646125 29.916562)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-49\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-53\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_17\">\r\n     <g id=\"line2d_33\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"328.864625\" xlink:href=\"#m6e036c1ac8\" y=\"199.70025\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"line2d_34\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"328.864625\" xlink:href=\"#m34329f3dd6\" y=\"38.99625\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_17\">\r\n      <!-- 16 -->\r\n      <g transform=\"translate(322.502125 29.916562)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-49\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-54\"/>\r\n      </g>\r\n   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style=\"stroke:#000000;stroke-width:0.8;\" x=\"364.576625\" xlink:href=\"#m34329f3dd6\" y=\"38.99625\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_19\">\r\n      <!-- 18 -->\r\n      <g transform=\"translate(358.214125 29.916562)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-49\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-56\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_20\">\r\n     <g id=\"line2d_39\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"382.432625\" xlink:href=\"#m6e036c1ac8\" y=\"199.70025\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"line2d_40\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"382.432625\" xlink:href=\"#m34329f3dd6\" y=\"38.99625\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_20\">\r\n      <!-- 19 -->\r\n      <g transform=\"translate(376.070125 29.916562)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-49\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-57\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_21\">\r\n     <g id=\"line2d_41\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"400.288625\" xlink:href=\"#m6e036c1ac8\" y=\"199.70025\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"line2d_42\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"400.288625\" xlink:href=\"#m34329f3dd6\" y=\"38.99625\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_21\">\r\n      <!-- 20 -->\r\n      <g transform=\"translate(393.926125 29.916562)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-50\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_22\">\r\n     <g id=\"line2d_43\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"418.144625\" xlink:href=\"#m6e036c1ac8\" y=\"199.70025\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"line2d_44\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"418.144625\" xlink:href=\"#m34329f3dd6\" y=\"38.99625\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_22\">\r\n      <!-- 21 -->\r\n      <g transform=\"translate(411.782125 29.916562)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-50\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-49\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_23\">\r\n     <g id=\"line2d_45\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"436.000625\" xlink:href=\"#m6e036c1ac8\" y=\"199.70025\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"line2d_46\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"436.000625\" xlink:href=\"#m34329f3dd6\" y=\"38.99625\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_23\">\r\n      <!-- 22 -->\r\n      <g transform=\"translate(429.638125 29.916562)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-50\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-50\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_24\">\r\n     <g id=\"line2d_47\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"453.856625\" xlink:href=\"#m6e036c1ac8\" y=\"199.70025\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"line2d_48\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"453.856625\" xlink:href=\"#m34329f3dd6\" y=\"38.99625\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_24\">\r\n      <!-- 23 -->\r\n      <g transform=\"translate(447.494125 29.916562)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-50\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-51\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_25\">\r\n     <g id=\"line2d_49\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"471.712625\" xlink:href=\"#m6e036c1ac8\" y=\"199.70025\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"line2d_50\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"471.712625\" xlink:href=\"#m34329f3dd6\" y=\"38.99625\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_25\">\r\n      <!-- 24 -->\r\n      <g transform=\"translate(465.350125 29.916562)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-50\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-52\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_26\">\r\n     <g id=\"line2d_51\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"489.568625\" xlink:href=\"#m6e036c1ac8\" y=\"199.70025\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"line2d_52\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"489.568625\" xlink:href=\"#m34329f3dd6\" y=\"38.99625\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_26\">\r\n      <!-- 25 -->\r\n      <g transform=\"translate(483.206125 29.916562)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-50\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-53\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_27\">\r\n     <g id=\"line2d_53\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"507.424625\" xlink:href=\"#m6e036c1ac8\" y=\"199.70025\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"line2d_54\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"507.424625\" xlink:href=\"#m34329f3dd6\" y=\"38.99625\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_27\">\r\n      <!-- 26 -->\r\n      <g transform=\"translate(501.062125 29.916562)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-50\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-54\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_28\">\r\n     <g id=\"line2d_55\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"525.280625\" xlink:href=\"#m6e036c1ac8\" y=\"199.70025\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"line2d_56\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"525.280625\" xlink:href=\"#m34329f3dd6\" y=\"38.99625\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_28\">\r\n      <!-- 27 -->\r\n      <g transform=\"translate(518.918125 29.916562)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-50\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-55\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_29\">\r\n     <g id=\"line2d_57\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"543.136625\" xlink:href=\"#m6e036c1ac8\" y=\"199.70025\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"line2d_58\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"543.136625\" xlink:href=\"#m34329f3dd6\" y=\"38.99625\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_29\">\r\n      <!-- 28 -->\r\n      <g transform=\"translate(536.774125 29.916562)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-50\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-56\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_30\">\r\n     <g id=\"line2d_59\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"560.992625\" xlink:href=\"#m6e036c1ac8\" y=\"199.70025\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"line2d_60\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"560.992625\" xlink:href=\"#m34329f3dd6\" y=\"38.99625\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_30\">\r\n      <!-- 29 -->\r\n      <g transform=\"translate(554.630125 29.916562)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-50\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-57\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_31\">\r\n     <g id=\"line2d_61\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"578.848625\" xlink:href=\"#m6e036c1ac8\" y=\"199.70025\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"line2d_62\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"578.848625\" xlink:href=\"#m34329f3dd6\" y=\"38.99625\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_31\">\r\n      <!-- 30 -->\r\n      <g transform=\"translate(572.486125 29.916562)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-51\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_32\">\r\n     <g id=\"line2d_63\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"596.704625\" xlink:href=\"#m6e036c1ac8\" y=\"199.70025\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"line2d_64\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"596.704625\" xlink:href=\"#m34329f3dd6\" y=\"38.99625\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_32\">\r\n      <!-- 31 -->\r\n      <g transform=\"translate(590.342125 29.916562)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-51\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-49\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_33\">\r\n     <g id=\"line2d_65\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"614.560625\" xlink:href=\"#m6e036c1ac8\" y=\"199.70025\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"line2d_66\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"614.560625\" xlink:href=\"#m34329f3dd6\" y=\"38.99625\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_33\">\r\n      <!-- 32 -->\r\n      <g transform=\"translate(608.198125 29.916562)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-51\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-50\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_34\">\r\n     <g id=\"line2d_67\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"632.416625\" xlink:href=\"#m6e036c1ac8\" y=\"199.70025\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"line2d_68\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"632.416625\" xlink:href=\"#m34329f3dd6\" y=\"38.99625\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_34\">\r\n      <!-- 33 -->\r\n      <g transform=\"translate(626.054125 29.916562)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-51\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-51\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_35\">\r\n     <g id=\"line2d_69\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"650.272625\" xlink:href=\"#m6e036c1ac8\" y=\"199.70025\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"line2d_70\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" 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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "# time is the total sample duration in ms\n",
    "time = 50\n",
    "\n",
    "# dt is the step size within the sample duration in ms\n",
    "dt = 1.0\n",
    "\n",
    "# num_steps is how many steps are generated based on the time and dt values\n",
    "num_steps = int(time/dt)\n",
    "\n",
    "# input data\n",
    "train_image = torch.FloatTensor([[80,70,60],[50,40,30],[20,10,0]])\n",
    "\n",
    "# show input image\n",
    "plt.matshow(train_image, cmap='binary')\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Y')\n",
    "plt.title('Input Image')\n",
    "plt.show()\n",
    "\n",
    "# print train data\n",
    "print(\"Input Datum:\")\n",
    "print(\"======================\")\n",
    "print(train_image)\n",
    "print()\n",
    "\n",
    "# probabilities\n",
    "print(\"Probabilities of Spiking for Each Element per time step:\")\n",
    "print(\"======================\")\n",
    "for element in train_image.flatten():\n",
    "    prob = (element.item() / train_image.max()) * 100\n",
    "    print(\"Probability for \"+str(element.item())+\" to spike per time step:\",str(round(prob.item()))+\"%\")\n",
    "print()\n",
    "\n",
    "# create encoder and encode input\n",
    "encoder = BernoulliEncoder(time=time, dt=dt)\n",
    "encoded_image = encoder(train_image)\n",
    "print(\"Encoded Datum:\")\n",
    "print(\"======================\")\n",
    "#print(encoded_image)\n",
    "print()\n",
    "\n",
    "# Look at input spiking activity.\n",
    "encoded_image = np.reshape(encoded_image,(num_steps,train_image.nelement())).T\n",
    "plt.matshow(encoded_image, cmap='binary')\n",
    "plt.xlabel('Time')\n",
    "plt.ylabel('Neuron index')\n",
    "plt.title('Encoded Image Spiking Activity')\n",
    "plt.yticks(np.arange(train_image.nelement()))\n",
    "plt.xticks(np.arange(num_steps))\n",
    "plt.show()"
   ]
  },
  {
   "source": [
    "## 3e. Rank Order Encoder\n",
    "### Summary\n",
    "Encodes data via a rank order coding-like representation. One spike per neuron, temporally ordered by decreasing intensity. Inputs must be non-negative.\n",
    "\n",
    "### Rank Calculations\n",
    "1. Normalize data based on the max value\n",
    "2. Invert the data to get the times\n",
    "    * Higher Values correspond to Lower Times\n",
    "3. Divide the data by the max time\n",
    "    * Time values are rounded up to the next value and converted to int to get the ranks\n",
    "4. For each element, if the rank is within `time/dt` time steps, assign a spike to the time step corresponding to the rank\n",
    "\n",
    "### Limitations\n",
    "* Elements need to be widely varied to avoid rank overlap\n",
    "* The same rank can repeat multiple times"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 288x288 with 1 Axes>",
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      "Input Datum:\n======================\n[[100.  70.  50.]\n [ 40.  30.  20.]\n [ 15.  10.   5.]]\n\nRanks of Spiking for Each Element per time step:\n======================\nRank for 100.0 is: 2\nRank for 70.0 is: 2\nRank for 50.0 is: 3\nRank for 40.0 is: 4\nRank for 30.0 is: 5\nRank for 20.0 is: 7\nRank for 15.0 is: 9\nRank for 10.0 is: 13\nRank for 5.0 is: 25\n\nEncoded Datum:\n======================\n\n"
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     "text": [
      "Rank Plot:\n"
     ]
    },
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     "output_type": "display_data",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "# time is the total sample duration in ms\n",
    "time = 25\n",
    "\n",
    "# dt is the step size within the sample duration in ms\n",
    "dt = 1.0\n",
    "\n",
    "# num_steps is how many steps are generated based on the time and dt values\n",
    "num_steps = int(time/dt)\n",
    "\n",
    "# input data\n",
    "train_image = torch.FloatTensor([[100,70,50],[40,30,20],[15,10,5]])\n",
    "\n",
    "# show input image\n",
    "plt.matshow(train_image, cmap='binary')\n",
    "plt.xticks(())\n",
    "plt.yticks(())\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Y')\n",
    "plt.title('Input Image')\n",
    "plt.show()\n",
    "\n",
    "# print train data\n",
    "print(\"Input Datum:\")\n",
    "print(\"======================\")\n",
    "print(train_image.numpy())\n",
    "print()\n",
    "\n",
    "# ranks\n",
    "print(\"Ranks of Spiking for Each Element per time step:\")\n",
    "print(\"======================\")\n",
    "datum = train_image.clone()\n",
    "datum = (datum / datum.max()).flatten()\n",
    "times = torch.zeros(datum.numel())\n",
    "times[datum != 0] = 1 / datum[datum != 0]\n",
    "times *= time / times.max()\n",
    "times = torch.ceil(times).long()\n",
    "for idx in range(len(train_image.flatten().tolist())):\n",
    "    elements = train_image.flatten().tolist()\n",
    "    print(\"Rank for \"+str(round(elements[idx],2))+\" is:\",str(times[idx].item()))\n",
    "print()\n",
    "\n",
    "# create encoder and encode input\n",
    "encoder = RankOrderEncoder(time=time, dt=dt)\n",
    "encoded_image = encoder(train_image.clone())\n",
    "print(\"Encoded Datum:\")\n",
    "print(\"======================\")\n",
    "print()\n",
    "\n",
    "# Look at input spiking activity.\n",
    "encoded_image = np.reshape(encoded_image,(num_steps,train_image.nelement())).T\n",
    "plt.matshow(encoded_image, cmap='binary')\n",
    "plt.xlabel('Time')\n",
    "plt.ylabel('Neuron index')\n",
    "plt.title('Encoded Image Spiking Activity')\n",
    "plt.yticks(np.arange(train_image.nelement()))\n",
    "plt.xticks(np.arange(num_steps))\n",
    "plt.show()\n",
    "\n",
    "print(\"Rank Plot:\")\n",
    "max_intensity = int(train_image.max().numpy())\n",
    "x = torch.arange(1,max_intensity,1).float()\n",
    "plt.ylabel('Input Rank')\n",
    "plt.xlabel('Input Intensity')\n",
    "plt.title('Input Rank vs Input Intensity')\n",
    "x_times = (1/(x / max_intensity))\n",
    "x_times_max = x_times.max().numpy()\n",
    "x_times *= (time/dt) / x_times_max\n",
    "ranks = torch.ceil(x_times).long()\n",
    "plt.scatter(x,ranks)\n",
    "plt.show()"
   ]
  },
  {
   "source": [
    "## Future Modifications\n",
    "* Change the rank order coding add an option for each element having their own rank\n",
    "* Add population coding methods\n",
    "* Add inter-spike interval (ISI) encoding"
   ],
   "cell_type": "markdown",
   "metadata": {}
  }
 ]
}